A student is taking a multiple-choice exam in which eachquestion has four choice

Question

A student is taking a multiple-choice exam in which eachquestion has four choices. Assuming that she has no knowledge ofthe correct answers to any of the questions, she has decided on astrategy in which she will place four balls (marked A,B,C and D)into a box. She randomly selects one ball for each question andreplaces the ball in the box. The marketing on the ball willdetermine her answer to the question. There are five multiplechoice questions on the exam. What is the probability that she willget

A)   five questions correct?

B)    At least four questions correct?

C)    No questions correct

D)   No more than two questions correct?

Explanation / Answer

each question, she has 4 choices, so she have 1/4=25% chance to getit correct. (and 0.75, 75% to get it wrong) a). 5 question correct=0.25^5=0.0009766 b). at least 4 Q correct =P(4 questions correct ) + P( 5 questions correct) =0.25^4 + 0.25^5 =0.0048828 c).no question correct =0.75^5 =0.2373 d).no more than 2 Q correct = 1 correct + 2 question correct + none correct =0.25+0.25^2+0.75^5 =0.5498

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